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3 years ago

The first term of an arithmetic sequence is 4 and the tenth term is 67.

Mathematics

1 answer:

serg [7]3 years ago

8 0

Answer:

d = 7

Step-by-step explanation:

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Give a₁₀ = 67 and a₁ = 4 , then

a₁ + 9d = 67

4 + 9d = 67 ( subtract 4 from both sides )

9d = 63 ( divide both sides by 9 )

d = 7

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makkiz [27]

Answer:

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Explanation:

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250

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250

100

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Step-by-step explanation:

7 0

3 years ago

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mote1985 [20]

Answer:

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Step-by-step explanation:

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4 0

3 years ago

Read 2 more answers

In the triangle EFG,

MariettaO [177]

Answer:

$4.\ \sin E = \cos G$

Step-by-step explanation:

Given

$\triangle EFG$

$\angle F = 90^o$ --- right angle

Required

Which of the options is true

In a triangle, we have:

$\angle E + \angle F + \angle G = 180^o$ --- angles in a triangle

Substitute $\angle F = 90^o$

$\angle E + 90^o + \angle G = 180^o$

Collect like terms

$\angle E + \angle G = 180^o -90^o$

$\angle E + \angle G =90^o$

This implies that E and G are complementary angles.

For complementary angles, E and G;

$\sin E = \cos G$ and $\sin G = \cos E$

<em>Hence, (4) is true</em>

7 0

3 years ago

A rug has an area of 122.12 square feet. The rug is 8.7 feet wide. To the nearest hundredth, how many feet long is the rug?

allochka39001 [22]

$Area=width*length\\\\
Area=122.12feet^2\\
width=8.7feet\\
122.12=8.7*length\ \ \ | divide\ by\ 8.7\\\\
length=14.04feet
$

4 0

3 years ago

In an effort to estimate the mean amount spent per customer for dinner at major Atlanta restaurant, data were collected for a sa

AysviL [449]

Answer:

Confidence Interval is (21.76928571,23.43071429)

Step-by-step explanation:

The Formula we are going to use is:

$P=\mu$ ± $z_{\alpha/2}*\frac{\sigma}{\sqrt{n}}$

Where:

μ is the mean of sample

σ is the standard deviation of population

n is the sample size

z is the distribution

In our case:

μ=$22.60,σ=$2.50

For 98% Confidence level, 1-α=98%

α=2%

α/2=1%=0.01

From Cumulative standardized Normal Distribution table

$z_{\alpha/2}$ =2.326

$P=\mu\±z_{\alpha/2}*\frac{\sigma}{\sqrt{n}}\\P=22.60\±2.326*\frac{2.50}{\sqrt{49}}\\P=22.60\±0.8307142857$

P=23.430714 P=21.769286

Confidence Interval is (21.76928571,23.43071429)

5 0

3 years ago